Negative Math: How Mathematical Rules Can be Positively BentA student in class asks the math teacher: "Shouldn't minus times minus make minus?" Teachers soon convince most students that it does not. Yet the innocent question brings with it a germ of mathematical creativity. What happens if we encourage that thought, odd and ungrounded though it may seem? Few books in the field of mathematics encourage such creative thinking. Fewer still are engagingly written and fun to read. This book succeeds on both counts. Alberto Martinez shows us how many of the mathematical concepts that we take for granted were once considered contrived, imaginary, absurd, or just plain wrong. Even today, he writes, not all parts of math correspond to things, relations, or operations that we can actually observe or carry out in everyday life. Negative Math ponders such issues by exploring controversies in the history of numbers, especially the socalled negative and "impossible" numbers. It uses history, puzzles, and lively debates to demonstrate how it is still possible to devise new artificial systems of mathematical rules. In fact, the book contends, departures from traditional rules can even be the basis for new applications. For example, by using an algebra in which minus times minus makes minus, mathematicians can describe curves or trajectories that are not represented by traditional coordinate geometry. Clear and accessible, Negative Math expects from its readers only a passing acquaintance with basic high school algebra. It will prove pleasurable reading not only for those who enjoy popular math, but also for historians, philosophers, and educators. Key Features?

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Negative math: how mathematical rules can be positively bent
Avis d'utilisateur  Not Available  Book VerdictIt's a rare person who describes negative numbers (or any numbers) as "unassuming but fun," and he is likely the same person who would notice that negative numbers "stand as just about the only kind ... Consulter l'avis complet
Table des matières
Introduction  1 
The Problem  10 
History Much Ado about Less than Nothing  18 
The Search for Evident Meaning  36 
History Meaningful and Meaningless Expressions  43 
Impossible Numbers?  66 
History Making Radically New Mathematics  80 
From Hindsight to Creativity  104 
Can Minus Times Minus Be Minus?  131 
Unity in Mathematics  166 
Making a Meaningful Math  174 
Finding Meaning  175 
Designing Numbers and Operations  186 
Physical Mathematics?  220 
notes  235 
further reading  249 
Math Is Rather Flexible  110 
Sometimes 1 Is Greater than Zero  112 
Traditional Complications  115 
acknowledgments  259 
261  